4 problems

Finiteness conjecture. If $M$ is atoroidal, then $M$ carries only finitely many isotopy classes of tight contact structures.

General slice-Bennequin inequality. $(Y,\xi)$ is tight if and only if

Let $(M,\xi)$ be a contact 3-manifold. Let $X_\alpha$ be a Reeb vector field and $J$ a complex structure on the contact distribution, and let $\theta'$ denote the instantaneous rot…

Let $(M^3,\xi)$ be a closed contact manifold admitting a contact form $\alpha$ and a complex structure $J$ on $\xi$ such that … everywhere, where $X_\alpha$ is the Reeb field of…